AGES 10 - 13

Introduction to Algebra

A thorough introduction to Algebra for students in grades 6-9 who have completed our Pre-Algebra class. This course is designed to give students a strong foundation in the Algebra concepts that will be built on in subsequent courses. The curriculum focuses on inequality and system of equations; ratios, percent, and proportions; linear functions; factoring, quadratic equations, and functions; general functions, sequence, and series; polynomials, exponentials, and logarithms. Students will be prepared to tackle more advanced Algebra learning.

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Who is this course for
This course is for students who have some previous beginner Algebra experience or have completed our Pre-Algebra course.
This course typically takes 3-6 months to complete. This depends on the student's experience and how fast they can master the concepts and the knowledge. Our instructors move at the pace of the student, it may take extra time for some students to reinforce what they have learned.
Curriculum
Chapter 1: Follow the rules
Review of arithmetic, exponents and radicals
Chapter 2: X marks the spots
Operations on algebraic expressions (distribution, addition/subtraction)
Chapter 3: Linear Equation
Solving linear equations and word problems
Chapter 4: More variables
Operations on algebraic expressions with more than one variable
Chapter 5: Multi-variable linear equations
Solving system of equations with two equations in two variables
Chapter 6: Ratios and Percents
Challenging problems on ratios and percents
Chapter 7: Proportion
Direct, inverse, and joint proportions
Chapter 8: Graphing Lines
Properties of the graph of the line y=ax+b
Chapter 9: Introduction to Inequalities
Comparing two numbers, Linear Inequalities
Chapter 10: Quadratic Equations I
Solving quadratic equations by factoring, Vieta’s formulae
Chapter 11: Special Factorizations
Squares and difference of squares, sum and difference of cubes, rationalizing denominators
Chapter 12: Quadratic Equations II
Solving quadratic equations by completing the squares and using the quadratic formula
Chapter 13:Graphing Quadratics
Properties of the graphs of parabolas y=ax^2+bx+c and circles x^2+y^2=r^2
Chapter 14: More Inequalities
Quadratic Inequalities, Trivial and AM-GM Inequality
Chapter 15: Functions
Definition of functions, composition and inverse of functions
Chapter 16: Graphing Equations
Properties of graphs of functions, transformation of functions
Chapter 17: Polynomials
Addition, subtraction, and multiplication of polynomials.
Chapter 18: Exponents and Logarithms
Exponents, Logarithms, interest
Chapter 19: Special Functions
Radicals, absolute value, floor and ceiling, rational functions, and piecewise functions
Chapter 20: Sequence and series
Arithmetic and geometric sequence and series
Chapter 21: Special Manipulations
More techniques to solve equations by exploiting the self-similarity and symmetry of the problems
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